Given his desire to continue toward a Ph.D., Ryan originally decided not to play professional football after the Rams chose him in the fifth round of the 1958 NFL Draft. However, he changed his mind after he was able to enroll at both UCLA and University of California, Berkeley in pursuit of the advanced degree. Ryan then transferred back to Rice, where he studied during the off-season.[3]

Ryan spent the first four years of his career primarily in a reserve capacity, making $12,000 per year.[3] He did start a handful of games in competition with teammates Billy Wade and Zeke Bratkowski. In 1961, he and future Hall of FamerOllie Matson connected on a 96-yard touchdownreception, establishing a new team record. However, after sitting on the bench for the last four games of the 1961 season, Ryan stormed into the dressing room and threatened General Manager Elroy Hirsch that he was going to quit football if he were not traded. He became part of a multi-player deal with the Browns on July 12, 1962, his 26th birthday, as the arrival of highly touted newcomer Roman Gabriel made Ryan expendable.

In 1964, Ryan established himself as one of the league’s best passers. He threw for 2,404 yards and repeated his 1963 performance by completing 25 touchdown passes, which was enough to lead the league. Ryan had excellent company on the Browns offense: fullbackJim Brown; wide receivers Collins and Paul Warfield; and an outstanding offensive line led by future Hall of Famers Lou Groza and Gene Hickerson. But Ryan was also a clutch performer during the Browns’ memorable 10–3–1 season. Needing a win in the December 12 regular season finale against the New York Giants to clinch a berth in the NFL title game, Ryan completed 12 of 13 passes for five touchdowns and ran for a sixth touchdown in the 52–20 win. Two weeks later in the championship game against the Baltimore Colts, Ryan hit Collins for three touchdowns to win the title, 27–0 (the last Browns championship to date).

Ryan was rewarded for his performance with the first of three straight Pro Bowl appearances. Unfortunately, on the first play of the second half, he suffered a severe shoulder injury in the game after the combined 800-pound trio of PackerWillie Davis, LionRoger Brown and ColtGino Marchetti converged on the signal caller. Speculation persists to this day that Marchetti went out of his way to injure Ryan due to the perception that the quarterback ran up the score in the championship, with Marchetti's statement that he wanted "one more shot" at Ryan also fueling the rumors. However, a study of the film by Cleveland coaches in the weeks after the game exonerated Marchetti.

After winning the championship, Art Modell raised his salary $25,000, up from about $18,000 per season.[3]

Ryan’s numbers dropped in 1965, throwing for only 1,751 yards and 18 touchdowns. While his shoulder had completely healed, a sore elbow in training camp and an injured arch early in the regular season played a role in his completing fewer than half of his passes during the campaign. Those struggles resulted in a continuing cool relationship with Browns' fans, who booed him often during home contests. Part of Ryan's decline can also be traced to the absence of second-year wide receiver Paul Warfield, who missed much of the season after suffering a double fracture of the collarbone in the team's first exhibition game.

In 1966, he bounced back with a superb season, leading the league with 29 touchdown passes and finishing second with 2,976 yards despite playing with intense pain. Ryan's output helped alleviate the absence of the legendary Jim Brown, who had retired prior to the start of training camp. His 29 touchdown passes in 14 games ranks second in Browns franchise history to Brian Sipe, who got 30 in a 16-game 1980 season.[4]

On January 25, 1967, Ryan underwent an operation to repair the remaining effects of his injury. The surgery eliminated the pain, but also affected his throwing motion. In the 1967 season opener, Ryan's injury woes continued as he sprained both ankles in a 21–14 loss to the Dallas Cowboys. Battling through that malady, along with shoulder and knee troubles, Ryan led the team to a 9–5 record to reach the playoffs. The season would see Ryan having a concussion from a head-to-head collision with Dick Butkus. He was knocked out in the second-quarter but came back to throw three touchdown passes in the third quarter to will his team to a 24-0 victory. Ryan credits this collision for the cervical disc replacement he underwent after retiring.

Ryan's tenure as the Browns' starting quarterback came to an abrupt end following a 1–2 start to the 1968 season. Browns' head coachBlanton Collier replaced Ryan with Bill Nelsen, who went on to lead the team to a division title. The official conclusion of Ryan's time with the Browns came on September 9, 1969 when he was released, but new Redskins' coach Vince Lombardi quickly signed Ryan as a backup.

Despite throwing only one pass during the 1969 season, Ryan returned for the last of his 13 years in the NFL in 1970 before officially announcing his retirement on April 13, 1971. With his accurate throwing arm, his 14.7 yards per completion still ranks as one of the all-time leaders.[4]

Ryan attended graduate school during the first part of his playing career, and in 1965, he earned his Ph.D. from Rice. He worked for seven postgraduate years under Dr. G. R. MacLane, one of the best geometric-function theorists, and produced the dissertation "Characterization of the Set of Asymptotic Values of a Function Holomorphic in the Unit Disc.[3]" In 1966, Ryan published two fundamental papers on the set of asymptotic values of a function holomorphic in the unit disc in Duke Mathematical Journal.[5]

He started teaching at Rice during his career and, during his time with the Browns, he became an assistant professor at the Case Institute of Technology in February 1967. Ryan had a full teaching load,[6] which includes undergraduate and graduate courses, and conducting research in complex analysis.[7][8] While at training camp, Ryan taught math in the morning and went to football practice in the afternoon.[9] Ryan taught his last course at Case Western Reserve in the spring of 1971. He was promoted to associate professor that summer. After taking a leave of absence for the next three years, he resigned his faculty position in 1974.

Ryan learned computer programming and software through the Chi Corp., Case Western Reserve’s then newly launched private computer company. He compiled advanced statistics to apply what he learned to football. The Browns was shown his results and liked the project but didn't offer the extra cash to move it forward.[3]

Ryan’s second career was fodder for many jokes by sportswriters. Red Smith wrote that the Browns' offense consisted of a quarterback who understood Einstein’stheory of relativity and ten teammates who didn’t know there was one. Ryan was somewhat put off by the focus on his academic life, as he considered himself to be a regular football player.

Soon after his retirement from the Redskins, Ryan remained in the nation's capital when he was named Director of Information Services for the U.S. House of Representatives. While there, he helped advance the computer age in politics by playing an integral role in establishing the body's first electronic voting system. This enabled voting procedures that usually ran for 45 minutes to be shortened to around 15 minutes. By the time he left the post, the office had an annual budget of eight million dollars with a staff of 225.[10]

Ryan resigned that post to become athletic director and lecturer in mathematics at Yale University on March 7, 1977. Ryan served in that position for ten years before resigning to become the school's Associate vice President for Institutional Planning.

He was a member of the Rice Board of Governors from 1972 to 1976, and Ryan was recognized as a distinguished alumnus in 1987. Ryan became vice president for external affairs at Rice in August 1990, increasing annual gifts to the university to a three-year average of $32.8 million for the fiscal years 1992–94 from $21.4 million for the fiscal years 1988–90. In 1995, he resigned his post as vice president for external affairs at Rice, owing to differences with President Malcolm Gillis concerning the future course of external affairs. Ryan ended his institutional career as a professor of mathematics, and professor of computational and applied mathematics at Rice.[11]

Ryan was president and chief executive officer of Contex Electronics, which designed and manufactured cable and interconnect products for the computer and communications industries. Ryan also served as director for America West Airlines, Sequoia Systems, and of Danielson Holding Corporation. He was an advisory director of United Medical Care Inc.[12]

Now retired, Ryan lives on 78 acres of heavily forested land[13] in Grafton, Vermont with his wife, Joan, a retired sportswriter and nationally syndicated columnist for the Washington Post.[3] In retirement, he now runs a sophisticated self-designed program that helps micro-analyze statistical behavior of the up-and-down pricing movement that underlies the pricing behavior of the futures market. He is also doing work on Oppermann's conjecture about the distribution of prime numbers.[3]

Another Browns quarterback received a "professional doctorate"; Dr. Dave Mays, DDS, played for the team in 1976 and 1977.

Ryan's career numbers (including years with the Rams and Redskins): 1,090 completions in 2,133 attempts for 16,044 yards, 149 touchdowns and 111 interceptions. Ryan also rushed for 1,358 yards and six touchdowns on 310 carries.